TITLE: Notation for eventually less than
QUESTION [8 upvotes]: Is there some existing notation for

\[f(n)\leq g(n)\] for sufficiently large n

Apart from just writing that itself?
I'm thinking of something compact like the Landau notation $f\ll g$.
(Apologies if this is too specific for MathOverflow - just close it if so. I was also unsure what tags to add, so just edit it accordingly).

REPLY [2 votes]: I agree with Joel Hamkins's answer, but I don't entirely agree with his comment on that answer.  I generally use asterisks to mean "with finitely many exceptions" or "modulo finite sets", so I'd use $f\leq^*g$ and $A\subseteq^*B$ as Joel says.  But when working modulo some ideal $I$ other than the ideal of finite sets, I'd ordinarily avoid asterisks and instead write $f\leq_Ig$ and $A\subseteq_IB$.
I'd like to protest vigorously against the use of $\ll$ in this situation.  To me, $f\ll g$ means that $f$ is a lot smaller than $g$ (at least eventually), whereas here you might have $f(n)=g(n)-1$ for all $n$.